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The recent questions about restarting rocket engines in space made me wonder about this. Every mission used the OMS a couple of times at least but rendezvous missions increased the usage. The record holder is probably some multiple rendezvous mission but I don't know a good source for this information.

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The OMS engines were built by Aerojet and were a member of the AJ10 engine family. They will be used on the Orion service modules (not new ones, the original ones built in the 70s (!)) and will be discarded when the service module is jettisoned.

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    $\begingroup$ Wikipedia states, uncited, "Each [OMS] engine could be reused for 100 missions and was capable of a total of 1,000 starts and 15 hours of burn time", so 10 starts on a mission is plausible -- counting 1-2 orbital insertion and 1 deorbit burn. $\endgroup$
    – Russell Borogove
    Aug 8, 2016 at 17:10

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After searching google for 'sts shuttle "OMS-10" burn', iterating with an increasing ID number, I think STS-39 is the record holder with some 16 OMS burns. (The burn count isn't precisely defined by the ID number, because OMS-1 is skipped on direct-insertion launches, and ascent-assist and deorbit burns aren't numbered.)

Interestingly, most of them are done with only one engine at a time; I don't know if you would count single versus double burns differently. STS-93 and STS-82 were also well above average and may have more individual OMS engine starts than -39.

https://id.scribd.com/mobile/doc/52642908/STS-39-Space-Shuttle-Mission-Report

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    $\begingroup$ Everything I see confirms this is the historical max (16 total burns, nine burns on each engine.) Long writeup on the mission at this link (although it seems to be down or at least super slow at the moment). ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110023479.pdf $\endgroup$
    – Organic Marble
    Aug 8, 2016 at 17:58

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